# A deep learning energy-based method for classical elastoplasticity

arXiv: https://arxiv.org/abs/2209.06467 · HTML: https://mlsanity.com/paper/2209.06467/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Sep 2022.

## Built on by (most cited first, 12 of 12)

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- [Energy-based physics-informed neural network for frictionless contact problems under large deformation](https://mlsanity.com/paper/2411.03671/) (2024)
- [LaDEEP: A Deep Learning-based Surrogate Model for Large Deformation of Elastic-Plastic Solids](https://mlsanity.com/paper/2506.06001/) (2025)
- [Differentiable Neural-Integrated Meshfree Method for Forward and Inverse Modeling of Finite Strain Hyperelasticity](https://mlsanity.com/paper/2407.11183/) (2024)
- [Applications of Scientific Machine Learning for the Analysis of Functionally Graded Porous Beams](https://mlsanity.com/paper/2408.02698/) (2024)
- [Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems](https://mlsanity.com/paper/2507.03660/) (2025)
- [Compliance Minimization via Physics-Informed Gaussian Processes](https://mlsanity.com/paper/2507.09968/) (2025)
- [FEM-Informed Hypergraph Neural Networks for Efficient Elastoplasticity](https://mlsanity.com/paper/2602.07364/) (2026)
- [A Hybrid Conditional Diffusion-DeepONet Framework for High-Fidelity Stress Prediction in Hyperelastic Materials](https://mlsanity.com/paper/2603.18225/) (2026)
- [A thermodynamically consistent physics-informed deep learning material model for short fiber/polymer nanocomposites](https://mlsanity.com/paper/2403.18310/) (2024)

## Abstract (arXiv)

The deep energy method (DEM) has been used to solve the elastic deformation of structures with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on the principle of minimum potential energy. In this work, we extend DEM to elastoplasticity problems involving path dependence and irreversibility. A loss function inspired by the discrete variational formulation of plasticity is proposed. The radial return algorithm is coupled with DEM to update the plastic internal state variables without violating the Kuhn-Tucker consistency conditions. Finite element shape functions and their gradients are used to approximate the spatial gradients of the DEM-predicted displacements, and Gauss quadrature is used to integrate the loss function. Four numerical examples are presented to demonstrate the use of the framework, such as generating stress-strain curves in cyclic loading, material heterogeneity, performance comparison with other physics-informed methods, and simulation/inference on unstructured meshes. In all cases, the DEM solution shows decent accuracy compared to the reference solution obtained from the finite element method. The current DEM model marks the first time that energy-based physics-informed neural networks are extended to plasticity, and offers promising potential to effectively solve elastoplasticity problems from scratch using deep neural networks.